Fractional Brownian motion in crowded fluids

Fractional Brownian Motion in Crowded Fluids – Supplement

Fluids for SPT experiments were obtained by dissolving dextran (500 kDa, Sigma) and sucrose (342 Da, Roth) in millipore water at concentrations of about 430 mg/ml (30% w/w) and 1500 mg/ml (60% w/w), respectively. Rhodamine-tagged tracer beads (50 nm, Polysciences) were added from a predissolved solution, resulting in a typical concentration of about 2 pM. Hence, 3-5 beads were observed in the f...

Lacunary Fractional Brownian Motion

In this paper, a new class of Gaussian field is introduced called Lacunary Fractional Brownian Motion. Surprisingly we show that usually their tangent fields are not unique at every point. We also investigate the smoothness of the sample paths of Lacunary Fractional Brownian Motion using wavelet analysis.

Tempered fractional Brownian motion

Fractional Brownian motion and data

We analyze the fractal behavior of the high frequency part of the Fourier spectrum of fBm using multifractal analysis and show that it is not consistent with what is measured on real traac traces. We propose two extensions of fBm which come closer to actual traac traces multifractal properties.

Simulation of fractional Brownian motion

Preface In recent years, there has been great interest in the simulation of long-range dependent processes, in particular fractional Brownian motion. Motivated by applications in communications engineering, I wrote my master's thesis on the subject in 2002. Since many people turned out to be interested in various aspects of fractional Brownian motion, I decided to update my thesis and make it p...